Mathematics > Numerical Analysis

Title:Computing tensor Z-eigenvectors with dynamical systems

Abstract: We present a new framework for computing Z-eigenvectors of general tensors
based on numerically integrating a dynamical system that can only converge to a
Z-eigenvector. Our motivation comes from our recent research on spacey random
walks, where the long-term dynamics of a stochastic process are governed by a
dynamical system that must converge to a Z-eigenvector of a transition
probability tensor. Here, we apply the ideas more broadly to general tensors
and find that our method can compute Z-eigenvectors that algebraic methods like
the higher-order power method cannot compute.